346 PRIME Opt. Maths Book - IX Specification Grid for Final Examination referred by CDC Nepal S.N. Containts Topics K-1 U-2 A-4 HA-5 TQ TM Periods 1 Algebra i. Relation ii. function iii. Polynomial iv. Sequence & Series 2 3 2 1 8 21 33 2 Limits & Continuity Limit & Continuity 1 – 1 – 2 5 10 3 Matrices i. Introduction ii. Addition iii. Multiplication 1 2 1 – 4 9 20 4 Co-ordinate Geometry i. Locus ii. Section Formula iii. Equation of Straight line iv. Area of Triangle 2 2 1 1 6 15 30 5 Trigonometry i. Measurement of Angle ii. Trigonometric Ratios iii. Conversion of TR iv. Standard Angles v. Certain Angles vi. Compound Angle 2 3 3 – 8 20 35 (4) 6 Vector i. Introduction ii. Vector Geometry 1 2 – 1 4 10 12 7 Transformation i. Reflection ii. Rotation iii. Translation iv. Enlargement 1 – 1 1 3 10 18 8 Statistics i. Partition Values ii. Quartile Deviation ii. Mean Deviation iii. Standard Deviation – 1 2 – 3 10 12 First Term Review 4 Second Term Review 4 Total Questions 10 13 11 4 38 34 Total Marks 10 26 44 20 100 170 K = Knowledge, U = Understanding, A = Application, HA = Higher ability
PRIME Opt. Maths Book - IX 347 Model Question Set for Final Terminal Examination Group : A [10 × 1 = 10] 1. a. If A × B = {(1, 3), (2, 4), (1, 4), (2, 3)} is the Cartesian product, find the sets A and B. b. If an+1 = 2an+2 – an , a0 = 2 and a1 = 4, find the value of a2 . 2. a. What is the limit value of the sequence 2.01, 2.001, 2.0001, 2.00001, ........ ? b. Write down the transpose of a matrix A = 2 1 1 3 < F. What type of matrix is it according to its transpose? 3. a. What is centroid of a triangle? Write down the co-ordiante of it. b. Find the slope and y-intercept of the straight line having equation 3 x – y = 3 4. a. Prove that Cos600° = – 2 1 b. If A + B = 4 r , Prove that (1 + TanA)(1 + TanB) = 2 5. a. What do you mean by position vector of a point? b. Find the image of a point (1, –2) under translation about T = 1 2 – < F. Group : B [13 × 2 = 26] 6. a. If f(x + 2) = 3x – 1, find f(x) and f(2). b. What must be subtracted from 2x3 – 3x2 + 2x – 1 to get x3 – 2x2 –3x + 2? c. If R = {(x, y) : 2x + y = 9, x, y ∈ N}, find ‘R’ in ordered pairs. 7. a. If aij = 3i – 2j is the general element of a matrix, find the matrix of order 2 × 2 and its transpose. b. If A = 1 1 2 – 3 < F, find the value of A2 – 3A + 5I where I is identity matrix of order 2 × 2. 8. a. Find the equation of locus of a point which moves so that it is equidistant from the points (1, 2) and (2, 1). b. If area of triangle having vertices (1, m), (4, 5) and (–2, 3) is 18 square units, find the value of ‘m’. 9. a. Prove that : Cos 8 r + Cos 8 3r + Cos 8 5r + Cos 8 7r = 0 b. If 1 – CosA = 2 1 , find the value of Cosec2 A – Cot2 A. c. Find the radius of a circle where an arc of length 13.2cm subtends an angle of 30° at the centre of the circle. 10. a. If a 3 3 = d n, find the magnitude and direction of a . b. Find OC in terms of a and b where c is the mid-point of AB. c. If R X X – = 200 and ∑f = 20, find the mean deviation and its coefficient where ∑X = 400. A B O b a c
348 PRIME Opt. Maths Book - IX Group : C [11 × 4 = 44] 11. If f(x) = 2x2 + 5x – 3, g(x) = x2 + 8x + 7 and f(x) = g(x), find the value of x. 12. If p(x) = x2 + 3x – 2 and q(x) = x + 3, find the value of p(x).q(x). Also divide the result so formed by x – 2. 13. Complete the table given below with limit value. x 0.9 0.99 0.999 0.9999 0.99999 ...................... f(x) = x x 1 1 – – 2 .............. .............. .............. .............. .............. .............. 14. If A = 2 3 1 –1 < F, B = 1 2 2 3 – < F and C = 3 1 1 2 < F, prove that A(B + C) = AB + AC. 15. Prove that y = mx + c as the equation of straight line. 16. The number of sides of two regular polygons are in the ratio 4:3 where difference of their interior angles is 15°. find the number of sides of the polygons. 17. Prove that : Cosq – Sinq + 1 Cosq + Sinq + 1 = – Cos 1 Sin i i 18. Prove that : Cos10° – Sin10° Cos10° + Sin 10° = Tan35° 19. Find the image of triangle having vertice (–2, –1), (1, 3) and (3, –2) under an enlargement about E[(1, –1), –2]. Also plot the object and image in graph. 20. Find 7th decile of the observations given below. x 12 169 28 32 20 24 36 f 5 10 12 9 14 15 10 21. Find the standard deviation and its coefficient of: x 15 20 25 30 35 f 6 8 12 10 4 Group : D [4 × 5 = 20] 22. Find the nth term of the sequence given below and write down in sigma notation. 2 1 3 2 5 3 – – + 8 4 12 5 + – 23. Find the equation of straight line passes through a point (1, 4) which cuts the line intercepted between the axes in the ratio 2:1. Also prove that it passes through the point (4, –2). 24. Prove that PQ BC 2 1 = and PQ | |BC from the adjoining diagram. 25. If a point A(2, 1) is translated to A’(5, 3) with a translation ‘T’, find the value of ‘T’. Also find the image of points B(3, –2) and C(5, 0) with T followed by rotation about 180° with centre (–2, 1) for DABC. Then plot the object and image in graph. Q C P B A